Question

All of these questions are about a normal deck of 52 cards

1. Suppose two cards are chosen without replacement. If we consider only the suits of the two cards, what is the sample space?

2. Suppose a single card is drawn. If we define events ? and ? as below, find ?(? or ?).

? = card is a spade ? = card is a king

3. Suppose again a single card is drawn from the deck. Define two events ? and ? that are disjoint (mutually exclusive).

Answer 1

Solution:

a) two cards are chosen without replacement. If we consider only the suits of the two cards,

There are 4 suits of 13 cards each , sample space for drawing two cards without replacement will be

4 * 13p2 = 13*12*4 = 624

b)

P(A) =P( card is spade) = 13/52

P(B) = P(card is a king) = 4/52

There's a card which is common for both event which is king of spade so, P(A and B) = 1/52

P(A or B) = P(A) +P(B) -P(A and B)

P(A or B) = 13/52 + 4/52 - 1/52 = 16/52 = 4/13

c) A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0

Example of two mutually exclusive event is as follow

Let A be the event of drawing a spade card

Let B be the event of drawing a red card.

So A = 13 spade cards

B= 26 red cards ( 13 of heart and 13 of diamond)

These event are mutually exclusive because there's no common card in both event.